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A novel denoising approach is proposed that is based on averaging reconstructed images. The approach first divides the spectrum of the image to be denoised into different parts. From every such partial spectrum is then reconstructed an image using a 2-D singularity function analysis model. By expressing each of the reconstructed images as the sum of the same noise-free image and a different smaller noise, the denoising is achieved through averaging the reconstructed images. The theoretical formulation and experimental results on both simulated and real images consistently demonstrated that the proposed approach can efficiently denoise while maintaining high image quality, and presents significant advantages over conventional denoising methods.